IMHO Dungeon Crawl is pretty much THE Roguelike these days. I haven't found anything nearly as well made as it. I've been playing it for the last 4 years and only recently got my babys first 3 runes ascension.
Feels good.

Are there any roguelikes with permadeath but without it being quite so easy to die? Preferably some kind of non-linear one where you're not just dungeon crawling all the time.

Permadeath kinda goes hand-in-hand with frequent death. The reason they feel like that, especially at first, is that you really have to use your head and employ every possible resource and play really carefully to keep yourself alive. Still, some of them (like IVAN) depend on you finding at least half-decent equipment in the first few minutes of the game or you'll just get killed shortly afterwards.

In this way I consider roguelikes a sort of cousin to the super-hard platformer genre, like Super Meat Boy and N. It's really easy to die in both, but the main distinguishing factor is that you die due to bad reflexes in a platformer, but you die due to bad planning in roguelikes. Getting good at a roguelike really is a process of trial-and-error.

I really want to get into stone soup, but it just seems way harder than any other roguelike I've played... Like the odds are always stacked against me. I'm also not terribly fond of the whole mechanic of identifying items and uncursing items, but I could potentially get used to that.

I think Elona is probably my favorite roguelike. It's possibly the most open-ended game I've played. You can pretty much beat the game playing as a pianist. Get high charisma, earn loads emone from playing at parties, hire bodyguards to do your fighting for you, charm/breed even stronger creatures to serve you. Or you could live the life of a pacifist, working as a traveling merchant and running/teleporting away from any danger.

Castle of the Winds
Oh MY GOD MY CHILDHOOD
I used to play the shit out of this, my sister and I would take turns. It was on a disc of "the 100 greatest shareware games" from like PC magazine.. LOVED IT.

Just got 8572 on crawl. Slowly working my way up. I only ever seem to do well as a warrior type, playing some brutish race like a minotaur. I killed Pikel in this run and got a +4 +2 electric whip from him. Shit was awesome.

Rogue Survivor is one of the easiest RLs I've played, I just collected as much food and ammo as possible, went into some building's basement (which conveniently has beds down there) and just camped the stairs, shotgunning every zombie's face off.

I Held out for 49 days before I ran out of food and thus had to go get some more, got fucked in the ass by an angry mob of pimps, bikers and zombies.

Rogue Survivor is one of the easiest RLs I've played, I just collected as much food and ammo as possible, went into some building's basement (which conveniently has beds down there) and just camped the stairs, shotgunning every zombie's face off.

I Held out for 49 days before I ran out of food and thus had to go get some more, got fucked in the ass by an angry mob of pimps, bikers and zombies.

Also am I the only one who never gets past level 2/3 because I try to explore every part of the dungeon?

I should think you'd survive an even shorter time if you DIDN'T explore every part of a floor. You might find more useful items if you keep exploring the floor, but if you advance before you find everything, you end up facing tougher monsters with worse equipment, fewer healing potions, etc.

Also am I the only one who never gets past level 2/3 because I try to explore every part of the dungeon?

You SHOULD explore every corner of the level and preferably (with possible exception of dangerous uniques and ghosts) kill every single enemy on a level before going on to the next one.
Every little bit of XP goes towards raising your skills that make you more powerful.

I just started playing Ascii sector, joined the Merchants, accepted the mission of delivering X amount of iron to some other planet. Do I need to buy all this iron for my money or load it on my ship from somewhere? When that will be answered - if I land with goods on the planet that ordered them - where do I unload it and get my pay?